Broadband Optical Constants and Nonlinear Properties of SnS2 and SnSe2

SnS2 and SnSe2 have recently been shown to have a wide range of applications in photonic and optoelectronic devices. However, because of incomplete knowledge about their optical characteristics, the use of SnS2 and SnSe2 in optical engineering remains challenging. Here, we addressed this problem by establishing SnS2 and SnSe2 linear and nonlinear optical properties in the broad (300–3300 nm) spectral range. Coupled with the first-principle calculations, our experimental study unveiled the full dielectric tensor of SnS2 and SnSe2. Furthermore, we established that SnS2 is a promising material for visible high refractive index nanophotonics. Meanwhile, SnSe2 demonstrates a stronger nonlinear response compared with SnS2. Our results create a solid ground for current and next-generation SnS2- and SnSe2-based devices.

Here, the objective of the present work is the comprehensive optical characterization of SnS 2 and SnSe 2 . Using spectroscopic ellipsometry and first-principle calculations, we determine the full broadband dielectric tensor of SnS 2 and SnSe 2 from ultraviolet to midinfrared wavelengths (300-3300 nm). The results demonstrate a high dielectric response (n > 3) with zero losses in a wide spectral range: 560-3300 nm for SnS 2 and 1300-3300 nm for SnSe 2 . Moreover, we measured the second-order nonlinear optical susceptibility of SnS 2 and SnSe 2 at wavelengths ranging from 750 to 1050 nm. Finally, our results revealed that SnS 2 is a high refractive index material, which fills the important gap in the visible spectrum between bandgap energies of GaP and TiO 2 , which makes SnS 2 a promising material for all-dielectric nanophotonics.

Surface and Structural Morphology Study
Thin films of SnS 2 and SnSe 2 were synthesized by the chemical vapor deposition (CVD) method and transferred on a quartz substrate. Figure 1a schematically illustrates the crystal structure of 1T-SnS 2 or SnSe 2 viewed along caxis and the a-axis. This crystal configuration is the most common atoms' arrangement for SnS 2 and SnSe 2 , where layers stack directly above one another [43,44]. Optical microscopy photographs in Figure 1b,f show the uniform substrate's coverage of synthesized SnS 2 and SnSe 2 films. Likewise, scanning electron microscopy (SEM) images in Figure 1c,g confirm the films' full-area coverage and homogeneity at the microscale. In addition, we checked the films' surface by atomic force microscopy (AFM), demonstrating an atomically smooth surface with root mean square (RMS) roughness of less than 1.6 nm and 0.5 nm for SnS 2 and SnSe 2 , respectively. Ultimately, we accurately measured the films' thickness via AFM topographical scans (Figure 1e,i). They yielded 20.0 ± 1.8 nm and 6.5 ± 0.7 nm thicknesses for SnS 2 and SnSe 2 films, correspondingly. terials 2022, 12, x FOR PEER REVIEW 2 of 12 [39,40], and photodetectors [41,42]. Hence, broadband linear and nonlinear optical properties are highly desired for the acceleration of the development of SnS2 and SnSe2based devices.
Here, the objective of the present work is the comprehensive optical characterization of SnS2 and SnSe2. Using spectroscopic ellipsometry and first-principle calculations, we determine the full broadband dielectric tensor of SnS2 and SnSe2 from ultraviolet to midinfrared wavelengths (300-3300 nm). The results demonstrate a high dielectric response (n > 3) with zero losses in a wide spectral range: 560-3300 nm for SnS2 and 1300-3300 nm for SnSe2. Moreover, we measured the second-order nonlinear optical susceptibility of SnS2 and SnSe2 at wavelengths ranging from 750 to 1050 nm. Finally, our results revealed that SnS2 is a high refractive index material, which fills the important gap in the visible spectrum between bandgap energies of GaP and TiO2, which makes SnS2 a promising material for all-dielectric nanophotonics.

Surface and Structural Morphology Study
Thin films of SnS2 and SnSe2 were synthesized by the chemical vapor deposition (CVD) method and transferred on a quartz substrate. Figure 1a schematically illustrates the crystal structure of 1T-SnS2 or SnSe2 viewed along c-axis and the a-axis. This crystal configuration is the most common atoms' arrangement for SnS2 and SnSe2, where layers stack directly above one another [43,44]. Optical microscopy photographs in Figure 1b,f show the uniform substrate's coverage of synthesized SnS2 and SnSe2 films. Likewise, scanning electron microscopy (SEM) images in Figure 1c,g confirm the films' full-area coverage and homogeneity at the microscale. In addition, we checked the films' surface by atomic force microscopy (AFM), demonstrating an atomically smooth surface with root mean square (RMS) roughness of less than 1.6 nm and 0.5 nm for SnS2 and SnSe2, respectively. Ultimately, we accurately measured the films' thickness via AFM topographical scans (Figure 1e,i). They yielded 20.0 ± 1.8 nm and 6.5 ± 0.7 nm thicknesses for SnS2 and SnSe2 films, correspondingly.  [44], optical microscopy images of (b) SnS2 and (f) SnSe2. SEM images of (c) SnS2 and (g) SnSe2. AFM scan images of (d) SnS2 and (h) SnSe2. AFM thickness measurements of (e) SnS2 and (i) SnSe2 films with characteristic step height profiles.

Analysis of the Crystal Structure and Raman Characterization
In nature, SnS2 and SnSe2 exist in several phase modifications [45,46], including 1T, 2H, 4H, and 18R polytypes. To identify the phase of our samples, we performed X-ray diffraction (XRD), whose spectra are displayed in Figure 2a,b. According to the Joint Committee on Powder Diffraction Standards (card No. 23-0677 and 89-2939) and previous publications [27,47,48], the obtained XRD patterns reveal the hexagonal lattice configuration, which could be 1T or 2H, for SnS2 and SnSe2 with lattice parameters a = b = 3.6486 Å and c = 5.8992 Å for SnS2 and a = b = 3.811 Å and c = 6.137 Å for SnSe2.  [44], optical microscopy images of (b) SnS 2 and (f) SnSe 2 . SEM images of (c) SnS 2 and (g) SnSe 2 . AFM scan images of (d) SnS 2 and (h) SnSe 2 . AFM thickness measurements of (e) SnS 2 and (i) SnSe 2 films with characteristic step height profiles.

Analysis of the Crystal Structure and Raman Characterization
In nature, SnS 2 and SnSe 2 exist in several phase modifications [45,46], including 1T, 2H, 4H, and 18R polytypes. To identify the phase of our samples, we performed X-ray diffraction (XRD), whose spectra are displayed in Figure 2a,b. According to the Joint Committee on Powder Diffraction Standards (card No. 23-0677 and 89-2939) and previous publications [27,47,48], the obtained XRD patterns reveal the hexagonal lattice configuration, which could be 1T or 2H, for SnS 2 and SnSe 2 with lattice parameters a = b = 3.6486 Å and c = 5.8992 Å for SnS 2 and a = b = 3.811 Å and c = 6.137 Å for SnSe 2 .
1T and 2H. Raman spectrum of SnS2 reveals out-of-plane vibration mode A1g at ~314 cm −1 and in-plane vibration of Eg at ~205 cm −1 , corresponding to 1T polytype [44,49,50]. Similar to SnS2, SnSe2 Raman spectrum has two characteristic phonon modes: A1g mode at ~185 cm −1 and Eg mode at ~116.5 cm −1 , associated with 1T-phase [36,51]. Moreover, Raman spectra at numerous locations of our samples demonstrate the same A1g and Eg peak positions, additionally validating the homogeneity of the studied SnS2 and SnSe2 thin films.

Optical Properties of SnS2 and SnSe2 Films
We investigated broadband optical constants of SnS2 and SnSe2 films through spectroscopic ellipsometry. We employed a two-layer optical model for ellipsometry data analysis: quartz substrate with SnS2 or SnSe2 film with the thickness determined from AFM (Figure 3e,i). Similar to other TMDCs [52,53], we describe SnS2 and SnSe2 dielectric function by the Tauc-Lorentz oscillator model (see Methods) [54,55]. Figure 3a,b shows the resulting optical constants n and k for SnS2 and SnSe2 films. Interestingly, we did not observe excitons for SnS2 and SnSe2, which can be explained by their indirect bandgap, in contrast, to the direct bandgap in MoS2 and WS2 [56,57]. Apart from the dielectric function, Tauc-Lorentz oscillator parameters allow us to obtain the positions of critical points of joint density of states: 3.91 eV (317 nm) for SnS2; 2.87 eV (432 nm) and 3.98 eV (311 nm) for SnSe2. Furthermore, SnS2 and SnSe2 both have zero absorption (k ~ 0) at a broad wavelength range, starting from 560 and 1300 nm (Figure 3a,b), respectively. For reference, we also plotted in Figure 3a,b refractive indices and bandgap transitions of SnS2 and SnSe2, determined by Domingo and coworkers [26]. As expected, the fundamental Aside from XRD characterization, we utilized Raman spectroscopy at 532 nm excitation wavelength (Figure 2c,d) to distinguish between two hexagonal configurations, 1T and 2H. Raman spectrum of SnS 2 reveals out-of-plane vibration mode A 1g at~314 cm −1 and in-plane vibration of E g at~205 cm −1 , corresponding to 1T polytype [44,49,50]. Similar to SnS 2 , SnSe 2 Raman spectrum has two characteristic phonon modes: A 1g mode at~185 cm −1 and E g mode at~116.5 cm −1 , associated with 1T-phase [36,51]. Moreover, Raman spectra at numerous locations of our samples demonstrate the same A 1g and E g peak positions, additionally validating the homogeneity of the studied SnS 2 and SnSe 2 thin films.

Optical Properties of SnS 2 and SnSe 2 Films
We investigated broadband optical constants of SnS 2 and SnSe 2 films through spectroscopic ellipsometry. We employed a two-layer optical model for ellipsometry data analysis: quartz substrate with SnS 2 or SnSe 2 film with the thickness determined from AFM (Figure 3e,i). Similar to other TMDCs [52,53], we describe SnS 2 and SnSe 2 dielectric function by the Tauc-Lorentz oscillator model (see Methods) [54,55]. Figure 3a,b shows the resulting optical constants n and k for SnS 2 and SnSe 2 films. Interestingly, we did not observe excitons for SnS 2 and SnSe 2 , which can be explained by their indirect bandgap, in contrast, to the direct bandgap in MoS 2 and WS 2 [56,57]. Apart from the dielectric function, Tauc-Lorentz oscillator parameters allow us to obtain the positions of critical points of joint density of states: 3.91 eV (317 nm) for SnS 2 ; 2.87 eV (432 nm) and 3.98 eV (311 nm) for SnSe 2 . Furthermore, SnS 2 and SnSe 2 both have zero absorption (k~0) at a broad wavelength range, starting from 560 and 1300 nm (Figure 3a,b), respectively. For reference, we also plotted in Figure 3a,b refractive indices and bandgap transitions of SnS 2 and SnSe 2 , determined by Domingo and coworkers [26]. As expected, the fundamental absorption edge coincides with the forbidden indirect transitions (Figure 3a,b), supporting our results in Figure 3a,b. For additional verification, we also measured the transmittance spectra of our samples (Figure 3c,d) and compared them with the transfer matrix calculations [58], based on optical constants from Figure 3a,b. Evidently, calculated and measured transmittance agree well, thereby validating our n and k in Figure 3a,b. erials 2022, 12, x FOR PEER REVIEW 4 of 12 absorption edge coincides with the forbidden indirect transitions (Figure 3a,b), supporting our results in Figure 3a,b. For additional verification, we also measured the transmittance spectra of our samples (Figure 3c,d) and compared them with the transfer matrix calculations [58], based on optical constants from Figure 3a,b. Evidently, calculated and measured transmittance agree well, thereby validating our n and k in Figure 3a,b.  Table A1.
To retrieve the full dielectric tensor, we leveraged first-principle calculations (Methods). Figure 4 shows the resulting refractive index and extinction coefficient along the ab-plane (nab and kab) and c-axis (nc and kc). The first-principle calculations reproduce the shape of the experimental dielectric function and render the major optical features: a wide zero-absorption spectral range and high dielectric response. However, first-principle calculations overestimate values of dielectric function since the computations were performed assuming the ideal crystalline structure, whereas the studied CVD-grown films have a polycrystalline structure. Nevertheless, first-principle calculations provide access to the full dielectric permittivity tensor, allowing us to estimate the anisotropic optical properties, which are the most noticeable for SnS2 with birefringence Δn = nab − nc ≈ 0.3 and almost negligible for SnSe2. In contrast, ellipsometry is nearly insensitive to optical constants along the c-axis, as explained by Ermolaev and colleagues [56,59]. Thus, our computations reveal for the first time the optical anisotropy in SnS2 and SnSe2, which could be relevant in next-generation anisotropic nanophotonics [60]. For comparison, we included refractive indices (red circles) and electronic transitions (dashed lines) determined by Domingo et al. [26]. Measured and calculated transmittance for (c) SnS 2 and (d) SnSe 2 on quartz. Tabulated optical constants for SnS 2 and SnSe 2 are collected in Table A1.
To retrieve the full dielectric tensor, we leveraged first-principle calculations (Methods). Figure 4 shows the resulting refractive index and extinction coefficient along the ab-plane (n ab and k ab ) and c-axis (n c and k c ). The first-principle calculations reproduce the shape of the experimental dielectric function and render the major optical features: a wide zeroabsorption spectral range and high dielectric response. However, first-principle calculations overestimate values of dielectric function since the computations were performed assuming the ideal crystalline structure, whereas the studied CVD-grown films have a polycrystalline structure. Nevertheless, first-principle calculations provide access to the full dielectric permittivity tensor, allowing us to estimate the anisotropic optical properties, which are the most noticeable for SnS 2 with birefringence ∆n = n ab − n c ≈ 0.3 and almost negligible for SnSe 2 . In contrast, ellipsometry is nearly insensitive to optical constants along the c-axis, as explained by Ermolaev and colleagues [56,59]. Thus, our computations reveal for the first time the optical anisotropy in SnS 2 and SnSe 2 , which could be relevant in next-generation anisotropic nanophotonics [60].  In the light of the rapid development of nonlinear optical devices based on SnS2 and SnSe2 [36,37,61], we also measured their nonlinear optical response ( Figure 5). Specifically, we measured the second harmonic generation (SHG) in transmission geometry using 150 fs laser pulses focused into a 50 µm spot in diameter (see Methods). Figure 5a shows the SHG power dependence with the expected slope of 2 (2.01 ± 0.02 for SnS2 and 2.02 ± 0.04 for SnSe2), confirming the second-order nonlinear process and the absence of saturation effects. SHG spectra of SnS2 and SnSe2 are shown in Figure 5b. For SnSe2, SHG resonance is at 415 nm (2.98 eV), associated with the 2 photon direct transition at the critical point (2.87 eV) found above from ellipsometry measurements. The presence of SH signal at large pump wavelengths indicates the contribution of direct transitions with lower energies, meaning that the direct transition of SnSe2 is less than 2.36 eV. In contrast, for SnS2, the SH signal is negligible at large wavelengths. Therefore, the SHG resonance observed at the SH wavelength of 420 nm (2.95 eV) can be associated with the lowest energy direct transition of SnS2 in agreement with Domingo and colleagues' work [26].
To calculate the nonlinear optical susceptibility, we implemented the method, described in Boyd's book [62]. The technique relies on the following equation for the average power of SHG transmitted through sample: where ( ) is a nonlinear optical susceptibility, = 0.94 is the shape factor for Gaussian pulses, is the permittivity of vacuum, is the speed of light, = 80 MHz is the pulse repetition rate, = 150 fs is the pulse duration, = 25 µm is the focal spot radius, is a sample thickness, is a pump wavelength, Δ is the wavevectors mismatch of the pump and SH waves, and are refractive indices of material at pump and harmonic wavelengths, and ( ) and (2 ) are average power of the pump and the second harmonic radiation, respectively. In our case, the coherence length = /(4 − 4 ) of the observed processes is several hundred nanometers (from 300 nm to 900 nm for SnS2 and from 450 to 600 nm for SnSe2), which significantly exceeds the thickness of the films (Figure 1e,f). Thus, we can assume that the SHG is phase-matched and, hence, sinc (Δ /2) = 1. It allows us to evaluate SnS2 and SnSe2 nonlinear optical susceptibility, displayed in Figure 5c. In the light of the rapid development of nonlinear optical devices based on SnS 2 and SnSe 2 [36,37,61], we also measured their nonlinear optical response ( Figure 5). Specifically, we measured the second harmonic generation (SHG) in transmission geometry using 150 fs laser pulses focused into a 50 µm spot in diameter (see Methods). Figure 5a shows the SHG power dependence with the expected slope of 2 (2.01 ± 0.02 for SnS 2 and 2.02 ± 0.04 for SnSe 2 ), confirming the second-order nonlinear process and the absence of saturation effects. SHG spectra of SnS 2 and SnSe 2 are shown in Figure 5b. For SnSe 2 , SHG resonance is at 415 nm (2.98 eV), associated with the 2 photon direct transition at the critical point (2.87 eV) found above from ellipsometry measurements. The presence of SH signal at large pump wavelengths indicates the contribution of direct transitions with lower energies, meaning that the direct transition of SnSe 2 is less than 2.36 eV. In contrast, for SnS 2 , the SH signal is negligible at large wavelengths. Therefore, the SHG resonance observed at the SH wavelength of 420 nm (2.95 eV) can be associated with the lowest energy direct transition of SnS 2 in agreement with Domingo and colleagues' work [26].  Finally, we want to underline that SnS2 is a promising material for all-dielectric nanophotonics [63,64], demanding a high refractive index and low absorption. As shown in Figure 6, SnS2 meets both requirements since it possesses a refractive index n ≈ 2.8 and zero extinction in the visible and infrared ranges. More importantly, SnS2 could even compete with classical high refractive index materials such as Si, GaP, and TiO2 [65][66][67][68]. In particular, SnS2 has a wider transparency region compared with GaP and Si and a larger refractive index than TiO2 (Figure 6). More surprisingly, when we use the refractive index from first-principle calculations (Figure 4a) for monocrystalline SnS2, it perfectly fits into To calculate the nonlinear optical susceptibility, we implemented the method, described in Boyd's book [62]. The technique relies on the following equation for the average power of SHG transmitted through sample: where χ (2) is a nonlinear optical susceptibility, S = 0.94 is the shape factor for Gaussian pulses, 0 is the permittivity of vacuum, c is the speed of light, f = 80 MHz is the pulse repetition rate, τ = 150 fs is the pulse duration, r = 25 µm is the focal spot radius, L is a sample thickness, λ is a pump wavelength, ∆k is the wavevectors mismatch of the pump and SH waves, n ω and n 2ω are refractive indices of material at pump and harmonic wavelengths, and P(ω) and P(2ω) are average power of the pump and the second harmonic radiation, respectively. In our case, the coherence length L coh = λ/(4n 2ω − 4n ω ) of the observed processes is several hundred nanometers (from 300 nm to 900 nm for SnS 2 and from 450 to 600 nm for SnSe 2 ), which significantly exceeds the thickness of the films (Figure 1e,f). Thus, we can assume that the SHG is phase-matched and, hence, sin c 2 (∆kL/2) = 1. It allows us to evaluate SnS 2 and SnSe 2 nonlinear optical susceptibility, displayed in Figure 5c. Finally, we want to underline that SnS 2 is a promising material for all-dielectric nanophotonics [63,64], demanding a high refractive index and low absorption. As shown in Figure 6, SnS 2 meets both requirements since it possesses a refractive index n ≈ 2.8 and zero extinction in the visible and infrared ranges. More importantly, SnS 2 could even compete with classical high refractive index materials such as Si, GaP, and TiO 2 [65][66][67][68]. In particular, SnS 2 has a wider transparency region compared with GaP and Si and a larger refractive index than TiO 2 ( Figure 6). More surprisingly, when we use the refractive index from first-principle calculations (Figure 4a) for monocrystalline SnS 2 , it perfectly fits into the correlation line between the refractive indices and optical bandgaps of high refractive index materials (Figure 6c). Therefore, SnS 2 enables the essential spectral range of all-dielectric nanophotonics between GaP and TiO 2 . Finally, we want to underline that SnS2 is a promising material for all-dielectric nanophotonics [63,64], demanding a high refractive index and low absorption. As shown in Figure 6, SnS2 meets both requirements since it possesses a refractive index n ≈ 2.8 and zero extinction in the visible and infrared ranges. More importantly, SnS2 could even compete with classical high refractive index materials such as Si, GaP, and TiO2 [65][66][67][68]. In particular, SnS2 has a wider transparency region compared with GaP and Si and a larger refractive index than TiO2 ( Figure 6). More surprisingly, when we use the refractive index from first-principle calculations (Figure 4a) for monocrystalline SnS2, it perfectly fits into the correlation line between the refractive indices and optical bandgaps of high refractive index materials (Figure 6c). Therefore, SnS2 enables the essential spectral range of alldielectric nanophotonics between GaP and TiO2.

Materials
CVD-grown full-area coverage SnS2 and SnSe2 samples of thin films were purchased from 2d Semiconductors Inc. (2d Semiconductors Inc., Scottsdale, AZ, USA). The samples with an area of 1 × 1 cm 2 were grown by CVD on sapphire substrates and subsequently transferred on quartz substrates.

Materials
CVD-grown full-area coverage SnS 2 and SnSe 2 samples of thin films were purchased from 2d Semiconductors Inc. (2d Semiconductors Inc., Scottsdale, AZ, USA). The samples with an area of 1 × 1 cm 2 were grown by CVD on sapphire substrates and subsequently transferred on quartz substrates.

Surface Morphology Characterization
The surface morphology of SnS 2 and SnSe 2 thin films was analysed by an optical microscope (Nikon LV150, Tokyo, Japan) with a digital camera DS-Fi3, as well as the scanning electron microscope (SEM) using the acceleration voltage of 30 kV and different magnifications (JEOL JSM-7001F, Tokyo, Japan) to prove films homogeneity. The film surface morphology was studied by atomic force microscopy (AFM, notegra, Nt-MDT Spectrum Instruments, Moscow, Russia) in semi-contact mode using a silicon tip with a radius <10 nm and resonance frequency of~250 kHz (HA_NC Etalon, Tipsnano, Tallinn, Estonia) to determine surface roughnesses and films thicknesses.

Crystal Structure Characterization
X-ray diffraction (XRD) characterization was performed by X-ray diffractometer (ARL X'TRA, Thermo Fisher Scientific, Waltham, MA, USA) using Cu K α1 radiation line (λ = 1.54 Å) to analyze the crystal structure of the films using a regime of 2θ-scan with angles range of 5 • -75 • with a step of 0.05 • and accumulation time of 2 s.

Raman Characterization
The Raman spectra were measured with a confocal scanning Raman microscope Horiba LabRAM HR Evolution (HORIBA Ltd., Kyoto, Japan) with 532 nm linearly polarized excitation laser, 1800 lines/mm diffraction grating, and ×100 objective (N.A. = 0.90) using a spectra range of 100-450 cm −1 . The spectra were recorded with 3.5 mW incident laser power, with an integration time of 10 s and 10 spectra accumulation.

Ellipsometry Analysis
The optical constants n and k of SnS 2 and SnSe 2 were measured using a variable-angle spectroscopic ellipsometer (VASE, J.A. Woollam Co., Lincoln, NE, USA), working at room temperature, at variable incidence angles 30 • -75 • with a step of 5 • and wide spectral range from 300 to 3300 nm with a step of 1 nm, having the spotlight of size~1 mm around the center of the sample, utilizing the high precision optical alignment. To fit the measured ellipsometric parameters Ψ and ∆, we used the Tauc-Lorentz oscillator model was used, defined by the following formula: where E is the energy of the photon, A is the oscillator strength, C is the oscillator broadening, E g is the optical band-gap, E 0 is the oscillator central energy, and the real part of the dielectric function ε 1 was obtained from the imaginary part ε 2 using the Kramers-Kronig integration, plus ε ∞ , to account for high energy electronic transitions. For SnS 2 , we used one Tauc-Lorentz oscillator with the following parameters: A = 54.613 eV; C = 1.626 eV; E 0 = 3.911 eV; E g = 1.970 eV and ε ∞ = 5.031. For SnSe 2 , we used two Tauc-Lorentz oscillators with the following parameters: A 1 = 14.435 eV; C 1 = 1.345 eV; E 01 = 2.870 eV; A 2 = 20.432 eV; C 2 = 0.875 eV; E 02 = 3.981 eV; E g = 0.736 eV and ε ∞ = 4.445.

Optical Properties Characterization
Optical transmittance spectra of SnS 2 and SnSe 2 films on quartz were measured with a spectrophotometer (Cary 5000 UV-Vis-NIR, Agilent Tech., Santa Clara, CA, USA) at a wavelength range of 300-3300 nm.
The nonlinear optical properties of the sample were studied by a home-built multiphoton microscope [69], based on femtosecond Ti:sapphire laser (Coherent Chameleon Ultra 2, Santa Clara city, CA, USA) tunable in the spectral range from 680 to 1080 nm. The laser beam (80 MHz repetition rate, 150 fs pulse duration) was directed through the system, consisting of a half-wave plate on a motorized rotation stage and a Glan-Taylor prism, which provided control of the power and polarization of the incident radiation.
Then, the beam was focused on the sample surface with a 10 cm lens into a 50 µm spot. The sample was mounted on a 3-axis motorized stage (SigmaKoki, Tokyo, Japan) with a minimum step of 0.1 µm, which made it possible to accurately align the sample relative to the pump spot. The SH radiation generated by the sample was collected by an objective lens (N.A. = 0.95, 100x, Olympus, Tokyo, Japan) and directed to the detection channel consisting of a tube lens, filter (FGB39 Thorlabs, Newton, NJ, USA) to cut off the pump radiation, monochoromator, and a scientific CCD camera (Andor Clara, Belfast, United Kingdom). The SH signal was normalized over spectral functions of all optical elements in the detection channel including objective lens transmittance and detector sensitivity spectra. SHG spectra were measured at the same pump intensity for all wavelengths. The experimental setup was fully automated and situated in a black box.

First-Principle Calculations
The optical properties of SnS 2 and SnSe 2 were calculated using density functional theory (DFT) implemented in the Vienna Ab Initio Simulation Package [70,71]. Core electrons, their interaction with valence electrons, and exchange correlation effects were described within generalized gradient approximation [72] (Perdew-Burke-Ernzerhof functional) and the projector-augmented wave pseudopotentials [73]. The unit cell parameters were a = b = 3.6486 Å and c = 5.8992 Å for SnS 2 and a = b = 3.811 Å and c = 6.137 Å for SnSe 2 . The calculation was performed in two steps: first, the atomic positions of SnS 2 and SnSe 2 were relaxed in until the interatomic forces were less than 10 −3 eV/Å, and a 1-electron basis set was obtained from a standard DFT calculations. Second, the real and imaginary parts of frequency-dependent dielectric function were calculated using the GW approximation [74]. Cutoff energy of the plane waves basis set was set to 600 eV, and the Γ-centered 11 × 11 × 7 k-points mesh was used to sample the first Brillouin zone.

Conclusions
In conclusion, we theoretically and experimentally determined the anisotropic optical constants of SnS 2 and SnSe 2 in a wide spectral range (300-3300 nm). Our findings reveal a strong dielectric response of SnS 2 and SnSe 2 and their broad range with zero absorption. More importantly, for SnS 2 , this range includes visible frequencies, which makes SnS 2 a novel high refractive index material, which complements the classical high refractive index materials Si, GaP, and TiO 2 . Additionally, we measured the second-order nonlinear susceptibility of SnS 2 and SnSe 2 . From a broader perspective, our research enables a foundation for advanced optical engineering with SnS 2 and SnSe 2 .

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available upon reasonable request from the corresponding author.

Acknowledgments:
The authors thank MIPT's Shared Research Facilities Center for the use of their equipment.

Conflicts of Interest:
The authors declare no conflict of interest.
Appendix A Table A1. Tabulated optical constants for SnS 2 and SnSe 2 films from Figure 3a,b.